Need derivatives for function:
a) f(x)= ln(e^-x + 1/x)
a
$\displaystyle \frac{-(x-1)}{e^x+x}-\frac{1}{x}$
$\displaystyle \frac{-x^2+x-x-e^x}{xe^x+x^2}$
$\displaystyle \frac{-x^2-e^x}{xe^x+x^2}$
$\displaystyle \frac{ \frac{-x^2-e^x}{x^2e^x}}{ \frac{xe^x+x^2}{x^2e^x}}$
$\displaystyle \frac{ - \frac{1}{e^x} - \frac{1}{x^2}}{ \frac{1}{e^x} + \frac{1}{x}}$
$\displaystyle \frac{ -e^{-x} - \frac{1}{x^2}}{ e^{-x} + \frac{1}{x}}$
This argument follows a lot easier if you read it backwards, though.
I kind of like that simplification, though.